Solution

Let 

$S$ and $T$ represent MCL sprains and ACL tears, respectively.

Let $B$ be the event that player is backfield player.

Given:

$$$$\begin{matrix} P(S|B)= 0.39,& P(T|B)= 0.61,&P(S|B^c)= 0.33,& P(T| B^c)= 0.67,\\ P(B)= \dfrac{7}{15} \approx 0.47, &P(B|S \cup T)= 0.47,& P(B^c| S \cup T)= 0.43 \end{matrix}

a. Finding $P(S):$

$$$$\begin{align*} P(S) &= P(S \cap B) + P(S \cap B^c)\\ &= P(B) P(S|B) + P(B^c)(S| B^c)\\ &= 0.47 (0.39)+ 0.53(0.33)\\ &\approx 0.36 \end{align*}

Answer

a. $0.36$b. $0.49$ c. $0.45$

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